Equivalent Linearization of Generally Pinching Hysteretic, Degrading Systems

Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit ‘pinching’ of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model—an extension of the Bouc–Wen differential hysteresis model—is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies.